Math 2270
Quiz 8
This is a take home quiz. You are allowed to use any book, computer program, or other reference material that
you would like, but you are not allowed to consult any person but the instructor about these problems. This
includes your classmates. You are on your honor as far as this is concerned, but if I become aware of anyone
violating these rules, that person will recieve a zero for the quiz.
Since you have significantly more time to work on this quiz than an in-class quiz, I expect a little more out of
your presentation. When writing up your solutions to these problems, please use complete sentences and correct
mathematical statements. For examples of what I’d like, see my solutions to the in-class quizzes. Write your
solutions on separate paper that has no notebook edges. If you require more than one page, use real (not oragami)
staples to attach them together.
To receive credit, this quiz must be in my hands before I leave class on Friday, March 7, 2008.
1. Let V be an m-dimensional subspace of Rn and let T : V → V be the linear transformation defined by
T (~x) = c~x for a fixed scalar c. Let B be any basis for V . Find the matrix of T with respect to B.
2. Suppose that {~v1 , ~v2 , . . . , ~vn } is an orthonormal set in Rn . Let
A = [~v1~v2 · · · ~vn ].
Show that A is invertible.